Cold nuclear fusion

Abstract
Recent accelerator experiments on fusion of various elements have clearly demonstrated that the effective cross-sections of these reactions depend on what material the target particle is placed in. In these experiments, there was a significant increase in the probability of interaction when target nuclei are imbedded in a conducting crystal or are a part of it. These experiments open a new perspective on the problem of so-called cold nuclear fusion.

PACS.: 25.45 – deuterium induced reactions

Submitted to Physics of Atomic Nuclei/Yadernaya Fizika in Russian

Introduction
Experiments of Fleischmann and Pons made about 20 years ago [1], raised the question about the possibility of nuclear DD fusion at room temperature. Conflicting results of numerous experiments that followed, dampened the initial euphoria, and the scientific community quickly came to common belief, that the results of [1] are erroneous. One of the convincing arguments of skeptics was the lack in these experiments of evidence of nuclear decay products. It was assumed that “if there are no neutrons, therefore is no fusion.” However, quite a large international group of physicists, currently a total of about 100-150 people, continues to work in this direction. To date, these enthusiasts have accumulated considerable experience in the field. The leading group of physicists working in this direction, in our opinion, is the group led by Dr. M. McKubre [2]. Interesting results were also obtained in the group of Dr. Y. Arata [3]. Despite some setbacks with the repeatability of results, these researchers still believe in the existence of the effect of cold fusion, even though they do not fully understand its nature. Some time ago we proposed a possible mechanism to explain the results of cold fusion of deuterium [4]. This work considered a possible mechanism of acceleration of deuterium contaminant atoms in the crystals through the interaction of atoms with long-wavelength lattice vibrations in deformed parts of the crystal. Estimates have shown that even if a very small portion of the impurity atoms (~105) get involved in this process and acquires a few keV energy, this will be sufficient to describe the energy released in experiments [2]. This work also hypothesized that the lifetime of the intermediate nucleus increases with decreasing energy of its excitation, so that so-called “radiation-less cooling” of the excited nucleus becomes possible. In [5], we set out a more detailed examination of the process. Quite recently, a sharp increase of the probability of fusion of various elements was found in accelerator experiments for the cases when the target particles are either imbedded in a metal crystal or are a part of the conducting crystal. These experiments compel us to look afresh on the problem of cold fusion.

Recent experiments on fusion of elements on accelerators
For atom-atom collisions the expression of the probability of penetration through a Coulomb barrier for bare nuclei should be modified, because atomic electrons screen the repulsion effect of nuclear charge. Such a modification for the isolated atom collisions has been performed in H.J. Assenbaum and others [6] using static Born-Oppenheimer approximation. The experimental results that shed further light on this problem were obtained in relatively recent works C. Rolfs [7] and K. Czerski [8]. Review of earlier studies on this subject is contained in the work of L. Bogdanova [9]. In these studies a somewhat unusual phenomenon was observed: the sub-barrier fusion cross sections of elements depend strongly on the physical state of the matter in which these processes are taking place. Figure 1 (left) shows the experimental data [8], demonstrating the dependence of the astrophysical factor S(E) for the fusion of elements of sub-threshold nuclear reaction on the aggregate state of the matter that contains the target nucleus 7Li. The same figure (right) presents similar data [7] for the DD reaction, when the target nucleus was embedded in a zirconium crystal. It must be noted that the physical nature of the phenomenon of increasing cross synthesis of elements in the case where this process occurs in the conductor crystal lattice is still not completely clear.

Figure 1. Up – experimental data [8], showing the energy dependence of the S-factor for sub-threshold nuclear reaction on the aggregate state of matter that contains the nucleus 7Li. Down – the similar data [7] for the reaction of DD, when the target nucleus is placed in a crystal of zirconium. The data are well described by the introduction of the screening potential of about 300 eV.

The phenomenon is apparently due to the strong anisotropy of the electrical fields of the crystal lattice in the presence of free conduction electrons. Data for zirconium crystals for the DD reactions can be well described by the introduction of the screening potential of about 300 eV. It is natural to assume that the corresponding distance between of two atoms of deuterium in these circumstances is less than the molecular size of deuterium. In the case of the screening potential of 300 eV, the distance of convergence of deuterium atoms is ~510ˆ12 m, which is about an order of magnitude smaller than the size of a molecule of deuterium, where the screening potential is 27 eV. As it turned out, the reaction rate for DD fusion in these conditions is quite sufficient to describe the experimental results of McKubre and others [2]. Below we present the calculation of the rate process similar to the mu-catalysis where, instead of the exchange interaction by the muon, the factor of bringing together two deuterons is the effect of conduction electrons and the lattice of the crystal.

Calculation of the DD fusion rate for “Metal-Crystal” catalysis
The expression for the cross section of synthesis in the collision of two nuclei can be written as

where for the DD fusion

Here the energy E is shown in keV in the center of mass. S(E) astrophysical factor (at low energies it can be considered constant), the factor 1/E reflects de Broglie dependence of cross section on energy. The main energy dependence of the fusion is contained in an expression

that determines the probability of penetration of the deuteron through the Coulomb barrier. From the above expressions, it is evident that in the case of DD collisions and in the case of DDμcatalysis, the physics of the processes is the same. We use this fact to determine the probability of DD fusion in the case of the “metal-crystalline” DD-catalysis. In the case of DDμ- catalysis the size of the muon deuterium molecules (ion+) is ~5×10ˆ13m. Deuterium nuclei approach such a distance at a kinetic energy ~3 keV. Using the expression (1), we found that the ratio of σ(3.0 keV)/σ(0.3 keV) = 1.05×10ˆ16. It should be noted that for the free deuterium molecule this ratio [ σ(3.0keV)/σ(0.03keV)] is about 10ˆ73. Experimental estimations of the fusion rate for the (DDμ)+ case presented in the paper by Hale [10]:

Is this enough to explain the experiments on cold fusion? We suppose that a screening potential for palladium is about the same as for zirconium. 1 cmˆ3 (12.6 g) of palladium contains 6.0210ˆ23(12.6/106.4) = 0.710ˆ23 atoms. Fraction of crystalline cells with dual (or more) the number of deuterium atoms at a ratio of D: Pd ~1:1 is the case in the experiments [2] ~0.25 (e.g., for Poisson distribution). Crystal cell containing deuterium atoms 0 or 1, in the sense of a fusion reaction, we consider as “passive”. Thus, the number of “active” deuterium cells in 1 cmˆ3 of palladium is equal to 1.810ˆ22. In this case, in a 1 cmˆ3 of palladium the reaction rate will be

this corresponds to the energy release of about 3 kW. This is quite sufficient to explain the results of McKubre group [2]. Most promising version for practical applications would be Platinum (Pt) crystals, where the screening potential for d(d,p)t fusion at room temperature is about 675 eV [11]. In this case, DD fusion rate would be:

The problem of “nonradiative” release of nuclear fusion energy
As we have already noted, the virtual absence of conventional nuclear decay products of the compound nucleus was widely regarded as one of the paradoxes of DD fusion with the formation of 4He in the experiments [2]. We proposed the explanation of this paradox in [4]. We believe that after penetration through the Coulomb barrier at low energies and the materialization of the two deuterons in a potential well, these deuterons retain their identity for some time. This time defines the frequency of further nuclear reactions. Figure 2 schematically illustrates the mechanism of this process. After penetration into the compound nucleus at a very low energy, the deuterons happen to be in a quasi-stabile state seating in the opposite potential wells. In principle, this system is a dual “electromagnetic-nuclear” oscillator. In this oscillator the total kinetic energy of the deuteron turns into potential energy of the oscillator, and vice versa. In the case of very low-energy, the amplitude of oscillations is small, and the reactions with nucleon exchange are suppressed.

Fig. 2. Schematic illustration of the mechanism of the nuclear decay frequency dependence on the compound nucleus 4He* excitation energy for the merging deuterons is presented. The diagram illustrates the shape of the potential well of the compound nucleus. The edges of the potential well are defined by the strong interaction, the dependence at short distances Coulomb repulsion.

The lifetime of the excited 4He* nucleus can be considered in the formalism of the usual radioactive decay. In this case,

Here ν is the decay frequency, i.e., the reciprocal of the decay time τ. According to our hypothesis, the decay rate is a function of excitation energy of the compound nucleus E. Approximating with the first two terms of the polynomial expansion, we have:

Here ν° is the decay frequency at asymptotically low excitation energy. According to quantum-mechanical considerations, the wave functions of deuterons do not completely disappear with decreasing energy, as illustrated by the introduction of the term ν°. The second term of the expansion describes the linear dependence of the frequency decay on the excitation energy. The characteristic nuclear frequency is usually about 10ˆ22 sˆ-1. In fusion reaction D+D4He there is a broad resonance at an energy around 8 MeV. Simple estimates by the width of the resonance and the uncertainty relation gives a lifetime of the intermediate state of about 0.810ˆ22 s. The “nuclear” reaction rate falls approximately linearly with decreasing energy. Apparently, a group of McKubre [2] operates in an effective energy range below 2 keV in the c.m.s. Thus, in these experiments, the excitation energy is at least 4×10ˆ3 times less than in the resonance region. We assume that the rate of nuclear decay is that many times smaller. The corresponding lifetime is less than 0.3×10ˆ18 s. This fall in the nuclear reaction rate has little effect on the ratio of output decay channels of the compound nucleus, but down to a certain limit. This limit is about 6 keV. A compound nucleus at this energy is no longer an isolated system, since virtual photons from the 4He* can reach to the nearest electron and carry the excitation energy of the compound nucleus. The total angular momentum carried by the virtual photons can be zero, so this process is not prohibited. For the distance to the nearest electron, we chose the radius of the electrons in the helium atom (3.1×10ˆ11 m). From the uncertainty relations, duration of this process is about 10ˆ-19 seconds. In the case of “metal-crystalline” catalysis the distance to the nearest electrons can be significantly less and the process of dissipation of energy will go faster. It is assumed that after an exchange of multiple virtual photons with the electrons of the environment the relatively small excitation energy of compound nucleus 4He* vanishes, and the frequency of the compound nucleus decaying with the emission of nucleons will be determined only by the term ν°. For convenience, we assume that this value is no more than 10ˆ12-10ˆ14 per second. In this case, the serial exchange of virtual photons with the electrons of the environment in a time of about 10ˆ-16 will lead to the loss of ~4 MeV from the compound nucleus (after which decays with emission of nucleons are energetically forbidden), and then additional exchange will lead to the loss of all of the free energy of the compound nucleus (24 MeV) and finally the nucleus will be in the 4He ground state. The energy dissipation mechanism of the compound nucleus 4He* with virtual photons, discussed above, naturally raises the question of the electromagnetic-nuclear structure of the excited compound nucleus.

Figure 3 represents a possible energy structure of the excited 4He* nucleus and changes of its spatial configuration in the process of releasing of excitation energy. Investigation of this process might be useful to study the quark-gluon dynamics and the structure of the nucleus.

Discussion
Perhaps, in this long-standing history of cold fusion, finally the mystery of this curious and enigmatic phenomenon is gradually being opened. Besides possible benefits that the practical application of this discovery will bring, the scientific community should take into account the sociological lessons that we have gained during such a long ordeal of rejection of this brilliant, though largely accidental, scientific discovery. We would like to express the special appreciation to the scientists that actively resisted the negative verdict imposed about twenty years ago on this topic by the vast majority of nuclear physicists.

Dear Ing. Rossi,
thank you for yr. answer.
The phase transition of 2nd type has never been considered as a possible reason of solid state nuclear reaction .
Declaring this solid state effect as a possible candidate to explain the “anomalous” haet production, I am far from the intention to obtain informations on the e-cat.
My willingness was:
- to point out a simple way to test if this effect take place in the NiH during the heat emission (X ray diffraction);
- to point out that metal alloys or intermetallic compounds show the effect, so being potential places where an “anomalous” heat production can happen.
I want to finish with a provocation: given the earth core seems to contain Nickel. Hydrogen and produces heat are we all living on a ‘ante litteram’ e-cat?

Many thanks for your patience in answering our questions. I have already signed up for the 10KW e-cat. The following questions has cropped into my mind:

1. What would be the electrical input into the unit (electrical consumption)?
2. Would this be constant or modulating?
3. Would the unit be modulating or on a start/stop system so as to keep the temperature of the thermal load at the set-point required?

Do you already have a user’s technical data catalogue of the finished product, not revealing the secret technology of course, but just basic data on operation, setting up etc

I have signed on to purchase the home e-cat when it becomes available. I have a two quick questions in this regard. (1) Will these home units also come with the electrical conversion unit you are developing? (2) If not, will these home units be capable of accepting that capability when they do become available? Thank you and God speed with your wonderful work…

I found out about ECAT this morning and I have spent all day reading
everything I can find. Apparently 1 1MW Plant has been sold already
to an unknown entity, this is what the late October demonstration is for.

Not sure when the next orders for 1MW will go out.

I think this technology can help the debt crisis in the EuroZone and I
hope the sooner it becomes widely available the better.

Dear Propagare:
Please forward your suggestions directly to the website. I really have the seconds, not just the minutes, counted, as usual. Please send your request for the waiting list toinfo@leonardocorp1996.com
Warm Regards,
A.R.

please accept my apologize to try to uncover your first customer. My continuing work to spread the word with the same unbroken enthusiasm after all these months has paid his price.

Today I want to give you some information about the ecat.com website:
Please be aware that from my point of view there are several small bugs on ecat.com if you try to use the webform! I can’t reach someone by email so maybe you can. The errors occur when you try to buy (pre-order) one or more eCat’s Home from a German location.
You have got already an email with images attached to this issue at info@leonardocorp1996.com.

Very warm regards!

propagare

PS Please, if not already done, count me and my wife in for an eCat Home (send already by email to the address above), Thanks and Godspeed!

Can I order more than one e-cat? Would it be possible for me to integrate two or more 10KW e-cats myself by means of pipe-work, valves, sensors,PLC’s and other hardware? Thus satisfying thermal loads greater than 10KW?

Dear Alessandro Casali:
1- yes
2- for now you pay nothing. You will pay only after we will confirm the start of the production, if you will confirm the order. You will be totally free to cancel the order if you will not accept the purchasing conditions
Warm Regards,
A.R.

maybe i didn’t get your last message right, did you mean that as soon as you reach 10,000 bookings you will allow customers to confirm their orders at 400 EURO/THERMAL KW?

Does this mean customers will have to pay an earnest and will be bound to purchase?

I’m asking for clarification because i think you can reach that numer of booking pretty soon and i don’t think it would be that fair to let people pay (even a small earnest) before the home e-cat is completly ready for the market with all the certifications and authorisations in place.

I’m sure it’s just my misunderstanding and you will clarifiy my point.

Dear Felipe From Chile:
You are right, we are organizing this.
BY THE WAY: WE COLLECT FROM NOW THE NAMES OF ALL THE PERSONS OR ENITITES INTERESTED TO BUY AN E-CAT OF 10 KW. IF WE WILL REACH 10,000 NAMES IN THE LIST, THE PERSONS IN THE WAITING LIST WILL HAVE THE RIGHT TO CONFIRM OR NOT THEIR ORDER AT 400 EURO/THERMAL KW. DO NOT SEND MONEY, WE WILL ACCEPT THE ORDERS ONLY IF WE WILL REACH 10,000 NAMES IN THE WAITING LIST, COMBINING OUR LIST WITH THE WAITING LIST ORGANIZED BY OUR BROTHERS OF HYDROFUSION .
WARM REGARDS,
ANDREA ROSSI, LEONARDO CORP. (PRESIDENT)

Mr Rossi,
Having followed you for many months I decided to ask you a minor question, my apologies if it has been answered before. Since I am not a business man, I think one of the way to support your endevour is to become a qualified e-cat technician. In this context, Does your company have (or will have in the near future) training program for setup and maintenance of e-cat technology?. I think you will require qualified staff around the world pretty soon.

Dear “XY”:
I did not approve your comment, because contains very big stupidities, and I want not to expose you and your name to a bad portrait. But I want to answer to the acceptable questions you have posed, because I think the answers can be interesting for our Readers:
1- In the test of October 28th the water flow has been measured by the two flowmeters that the Consultant of the Customer has put just minutes before the test. He always checked the water flow, and the water trap that collected the non condensed water exiting form the output pipe
2- The Consultant is a 60 years person, who has 30 years of experience as engineer of military organizations; he is specialized in thermodynamics
3- As you can see from the reports, the temperature in the output pipe has always been more than 110 Celsius degrees during the self sustaining mode at room pressure.
A.R.
Warm Regards,
A.R.

Dear mr. Rossi, two questions:
- when you will disclose at least the basic theory of your e-cat? If I am not wrong, you were supposed to do it within last October
- are you going to disclose at least some of your new customer’s names, on my opinion this will be a great advertisement for both you and your clients
Thanks for you answer.
Luca Neri

Currently you guarantee a COP of 6:1 with your E-cat core. Do you see this as the upper limit or will it likely increase (for a single E-cat core) over the next few years? Similarly, the core must be changed out every 6 months. Is this likely to change to say once a year?

Dear Rossi,
you told to have found a customer who bought your 1MW e-cat. it seems it is National Technologie. but this firm declared that you are a customer for them, not thr contrary.
Can you explain that to us how many orders have you had from other customers and when you think you are delivering them?
I’m prayinf for your siccess!
Thanks
Giuseppe Vimercati

dear Andrea Rossi I pray for your safety n success for I feel the world is in dier need of cheep clean energy now. BUT don,t trust anyone I don.t even trust your your customer thay maybe and oil company dress like milatary buy e-cats then hide or distroy them. I don,t know. but I have an idea to help get patent sooner then later. maybe you like maybe not call it the Rossi challange to skeptics and the best of the best of energy engeneers and physicists.and forget about dri steam and all nitpicken spacifics OK how much water can you heat with a car battery or batteries in 2-3 hr before it dies covert to adapt to e-cat have one brand name battery make all your rules for them to try and do better then you. OK thats it that all i have but if you like the concept and it works for you maybe you could get me job working inside iam 27 years in trucking co and is getting cool outside.take good care of your self mike

Dear Ing. Rossi,
for a long time I have been trying to figure out a physical model to explain the “anomalous” heat production in the e-cat. It is some time I am convinced of a possible candidate: the phase transition of 2nd kind. This solid state effect, if it takes place in the single crystal of NiH at a certain temperature, could be responsible of an unsual proximity of an interstitial proton belonging to one of the coexisting structures with a Ni nucleus belonging to the other structure. A simple test to verify the presence of this effect could be an x ray diffraction test on a NiH sample producing “anomalous” heat. Additional things could be said but are worth of a direct contact.
Best regards
Aldo Soleri

The E-Cat uses isotopes of Nickel and ordinary Hydrogen as inputs. My understanding is that Deuterium does NOT react in this environment as it does in Palladium or other metals.

In self-sustainment mode, perhaps it is possible to stabilize the E-Cat by adding Deuterium or other gases to the Hydrogen. Rather than changing the Hydrogen pressure, if you change the mix of gases, or the isotope mixture of gases, the reaction might persist in self-sustainment longer than it does.

Adding Deuterium or other gases, may act as a brake (or sedative) to keep the reactivity from increasing, or at least reduce the rate of increase. Presumably, it is easier to start with the ‘right’ combination of gases that would maximize the duration of self-sustainment, than it would be to change the mixture of gases every few minutes.

Do you think adding other gases to the Hydrogen would have any effect, or is that just another way to reduce ordinary Hydrogen? ( Of course, you do not want the reaction to become more unstable ! )

Dear Alan:
My job is to work. I have to think to my job and only to it.
We already have Customers.
We are not ready to go public: my enterprise is still too risky to propose investments to the public: as I use to say, I want not to play foot-ball with the bones of the others.
The main lesson I got from my father is:” Think well before promising something, but once you said that you will do a thing, you have to do it”.
We will go public when and if I will be able to promise that the investment is sound.
Warm Regards,
A.R.